The distributional properties of the Moran coecient index (MC) measuring spatial autocorrelation ... more The distributional properties of the Moran coecient index (MC) measuring spatial autocorrelation were investigated by many authors, see e.g. [1]. The properties of MC for non-normal random variables were analysed by Grith in [2]. The general idea of that paper was to extend Pitman-Koopmans theorem for the mean and the variance of this index. The principal conclusion was that under independence assumption and big enough sample size the Pitman-Koopmans theorem results can be extended to some non-normal random variables. The independence and identically distributed property reduced the necessary sample size for this extension, as did the properties of symmetry and normal approximation. In the paper we continue the analysis performing simulations for randomly generated variables for the following distributions: beta, gamma, hypergeometric, inverse hypergeometric, log-normal, exponential, negative binomial, and t Student, as well as their mixtures and using Box-Cox power transformation.
Distance learning in all types of schools from March 2020 to the beginning of June 2021 (with a s... more Distance learning in all types of schools from March 2020 to the beginning of June 2021 (with a short break in September 2020) was forced by the COVID-19 pandemic. Previously, in Poland, this form of teaching was used sporadically, basically only for extra-curricular activities. The vast majority of teachers did not have any experience in this field. The large-scale introduction of new forms of distance learning and knowledge transfer and enforcement methods created a number of challenges and opened up new opportunities. The presented study attempts to identify the advantages and disadvantages of distance learning during the COVID-19 pandemic in the opinion of primary and secondary school teachers in the Wielkopolska region. The analysis was carried out based on empirical material obtained from questionnaires addressed to all teachers from the Wielkopolska region (703 questionnaires were received). The survey results allowed the diagnosis of positive and negative aspects of distance...
Introduction The anterolateral thigh flap (ALT) is one of the most commonly used grafts in head a... more Introduction The anterolateral thigh flap (ALT) is one of the most commonly used grafts in head and neck reconstructive surgery. In this type of surgery, it is essential that the vascular pedicle be long enough to ensure proper vascular anastomosis. However, it is difficult to accurately estimate the pedicle length preoperatively. In this context, the current study had two aims: (1) to assess the value of colour Doppler sonography (CDS) in the preoperative assessment of the vascular pedicle and (2) to develop a mathematical model to predict the length of the vascular pedicle based on the ultrasound findings. Materials and methods Retrospective review of patients who underwent primary surgery for head and neck cancer followed by ALT flap reconstruction at our institution from 2014 to 2018. All patients underwent CDS prior to surgical excision of the flap. Results Preoperative CDS was useful to identify the location of the vascular perforators, to estimate the pedicle length, and to identify the vascularization variant. Using the proposed mathematical formula, the estimated minimum pedicle length and actual length agreed in 73.9% of cases, increasing to 84.1% when a 5 mm margin of error was allowed. Moreover, preoperative ultrasound accurately distinguished the two anatomical variants of the ALT vasculature in nearly all cases (97.1%). Conclusion This study confirms the value of preoperative colour Doppler sonography for ALT flap reconstruction. The proposed mathematical model provides a highly accurate method of preoperatively assessing the length of the vascular pedicle, which may be of value in head and neck surgery.
Rozwój Regionalny i Polityka Regionalna, Mar 20, 2014
Zastosowanie metod taksonomicznych w analizie struktury systemu regionalnego Zarys treści: Celem ... more Zastosowanie metod taksonomicznych w analizie struktury systemu regionalnego Zarys treści: Celem pracy jest zastosowanie metod taksonomii numerycznej w badaniu makrostruktury regionalnej i ocena ich możliwości analitycznych. W pierwszej części pracy przedstawiono opis matematyczno-statystyczny dwóch metod: (1) metody delimitacji układów powiązań opartej na kryterium największego przepływu Nystuena i Daceya (1961), (2) metody identyfikacji istotnych relacji w systemie regionalnym na zasadzie maksymalizacji współczynnika determinacji, opracowanej przez Holmesa i Haggetta (1977). W drugiej części pracy wykorzystano równolegle proponowane metody dla określenia makrostruktury regionalnej Polski na podstawie międzyregionalnych przepływów migracyjnych. Dokonano również oceny wyników poznawczych uzyskanych w analizie makrostruktury regionalnej w aspekcie metodologicznym i empiryczno-diagnostycznym.
The findings presented in this paper are part of the comprehensive research carried out within th... more The findings presented in this paper are part of the comprehensive research carried out within the “Diversification of Social Attitudes in the Sphere of Educational Services during a Pandemic” project. This study examines the challenges that emerged during remote learning, focusing on parents’ involvement in their children’s learning process, as perceived by school principals. The conclusions are based on questionnaire interviews with principals of 36 randomly selected schools throughout the Wielkopolska region (Poland). The study spanned the second semester of the 2019/2020 school year and the first semester of 2020/2021. Several issues were identified in the interviews, including communication difficulties with students, lack of skills of teachers and students to work remotely, insufficient IT infrastructure at school and home, financial deficits impeding the purchase of new equipment, and a decline in students’ mental health. These problems were primarily related to the family (h...
Zróżnicowanie poziomu rozwoju i jego polaryzacja są silnie akcentowanymi cechami procesu rozwoju ... more Zróżnicowanie poziomu rozwoju i jego polaryzacja są silnie akcentowanymi cechami procesu rozwoju społeczno-gospodarczego zarówno w klasycznych koncepcjach rozwoju (zwłaszcza rozwoju spolaryzowanego), jak i w ich współczesnych kontynuacjach. Prowadzi to do występowania w przestrzeni ekonomicznej obszarów wzrostu i obszarów stagnacji gospodarczej. Dlatego niezwykle istotne jest poszukiwanie odpowiedzi na pytania dotyczące przyczyn zróżnicowań układów przestrzennych oraz procesów polaryzacji. Głównym celem pracy jest identyfikacja i analiza istotnych czynników determinujących rozmieszczenie oraz rozwój obszarów wzrostu i obszarów stagnacji gospodarczej w ujęciu całościowym i częściowym rozwoju, w układzie wybranych aspektów tego procesu. Procedurę identyfikacji czynników rozwoju oparto na analizie korelacji kanonicznych (ujęcie całościowe) oraz modelowaniu regresyjnym (ujęcie częściowe). Postępowanie badawcze przeprowadzono zarówno w układzie wszystkich powiatów, jak i ich specyficznych podukładów, tj. obszarów wzrostu i obszarów stagnacji gospodarczej. Słowa kluczowe: obszary wzrostu, obszary stagnacji, czynniki rozwoju, analiza kanoniczna, analiza regresji Wstęp Zróżnicowanie poziomu rozwoju i jego polaryzacja są silnie akcentowanymi cechami procesu rozwoju społeczno-gospodarczego zarówno w klasycznych koncepcjach rozwoju (zwłaszcza rozwoju spolaryzowanego), jak i w ich współczesnych kontynuacjach (por. Grzeszczak 1999, Churski 2011). Konsekwencją nasilających się procesów polaryzacji jest występowanie w przestrzeni ekonomicznej obszarów wzrostu i obszarów stagnacji gospodarczej (por. Churski 2013a). Dlatego niezwykle istotne jest poszukiwanie odpowiedzi na pytania 1 Artykuł powstał w ramach projektu badawczego "Rozwój społeczno-gospodarczy a kształtowanie się obszarów wzrostu i obszarów stagnacji gospodarczej" finansowanego ze środków Narodowego Centrum Nauki (N N306 791940), realizowanego przez zespół badawczy pracowników Zakładu Analizy Regionalnej Instytutu Geografii Społeczno-Ekonomicznej i Gospodarki Przestrzennej, którego członkami są autorzy.
Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic ac... more Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic activity based on geolocations of firms. The aim of the paper is to introduce theoretical backgrounds of SPAG. The measure is a product of two random variables with beta and gamma distributions. The moments of the product are described and estimated for Poland with spatial centroids of LAU2 treated as geolocations of firms for empirical distribution as well as for the set of firms located in a regular region. Another approach to SPAG properties has its origin in a geometric probability concept. We present the research results on geometric probability, applied to SPAG, as distance probability distributions for a regular region.
Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic ac... more Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic activity based on geolocations of firms. The aim of the paper is to introduce theoretical backgrounds of SPAG. The measure is a product of two random variables with beta and gamma distributions. The moments of the product are described and estimated for Poland with spatial centroids of LAU2 treated as geolocations of firms for empirical distribution as well as for the set of firms located in a regular region. Another approach to SPAG properties has its origin in a geometric probability concept. We present the research results on geometric probability, applied to SPAG, as distance probability distributions for a regular region.
To study urban heat island (UHI), Landsat 5 TM data and in situ measurements of air temperature f... more To study urban heat island (UHI), Landsat 5 TM data and in situ measurements of air temperature from nine points in Poznań (Poland) for the period June 2008-May 2013 were used. Based on data from measurement points located in different types of land use, the surface urban heat island (SUHI) maps were created. All available and qualitycontrolled Landsat 5 TM images from 15 unique days were used to obtain the characteristics of land surface temperature (LST) and UHI intensity. In addition, spatial analysis of UHI was conducted on the basis of Corine Land Cover 2006 dataset. In situ measurements at a height of 2 m above ground level show that the UHI is a common occurrence in Poznań with a mean annual intensity of 1.0°C. The UHI intensity is greater during the warm half of the year. Moreover, results based on the remote sensing data and the Corine Land Cover 2006 indicate that the highest value of the mean LST anomalies (3.4°C) is attained by the continuous urban fabric, while the lowest value occurs within the broad-leaved forests (−3.1°C). To recount from LST to the air temperature at a height of 2 m above ground level (T agl), linear and non-linear regression models were created. For both models, coefficients of determination equal about 0.80, with slightly higher value for the non-linear approach, which was applied to estimate the T agl spatial variability over the city of Poznań.
Contemporary changes of socioeconomic development factors. The aim of the work is to determine th... more Contemporary changes of socioeconomic development factors. The aim of the work is to determine the scope of contemporary changes of socioeconomic development factors, paying attention to the consequences for their interpretation and mechanism of impact relating to the regional and local level. The main goal is specified by formulating the following research questions: (1) What major megatrends shape contemporary developmental transformations? (2) What is the direction and scope of changes in socioeconomic development factors? (3) How are the conditions of development processes changing as a result of these changes and how they differentiate the processes of development in space? The article is a synthesis of the results of two research projects of the National Science Center: NN 306 79 19 40: Socioeconomic development and the development of areas of growth and areas of economic stagnation (2011–2014) and OPUS 10 – 2015/19/B/HS5/00012: New challenges of regional policy in shaping the factors of socioeconomic development of less developed regions (2016–2019) and the results of own authors' research – employees of the Regional Analysis Department at the Institute of SocioEconomic Geography and Spatial Management of the Adam Mickiewicz University in Poznań.
W artykule przedstawiono zastosowanie entropijnej statystyki Shannona i algorytmu opracowanego pr... more W artykule przedstawiono zastosowanie entropijnej statystyki Shannona i algorytmu opracowanego przez Semple’a i Gauthier w badaniu zmian w zróżnicowaniuregionalnym Polski. Dokonano oceny wartości poznawczej tej metody ze względu na możliwość analizy relacji między nierównościami między- i wewnątrzregionalnymi.The article presents the use of Shannon entropy statistics and algorithm developed by Semple and Gauthier in the study of changes in the Polish regional differences. The assessment of the cognitive value of this method due to the possibility of analyzing the relationship between inter- and intraregional inequalities is shown
Dynamicznemu rozwojowi uslug, jaki nastepuje w Polsce od początku lat 90. XX w., towarzyszą przem... more Dynamicznemu rozwojowi uslug, jaki nastepuje w Polsce od początku lat 90. XX w., towarzyszą przemiany związane ze strukturą sektora uslug. Analiza zmian zachodzących w gospodarce prowadzi do wniosku, ze coraz wiekszego znaczenia w sektorze uslug nabierają uslugi wyspecjalizowane, zatrudniające pracownikow o wysokich kwalifikacjach zawodowych, wśrod nich uslugi o wysokim nasyceniu wiedzą oraz grupa uslug dla producentow i dla biznesu. Celem pracy jest prezentacja przemian zachodzących w sektorze uslug w Polsce na tle innych panstw Europy. Analiza zmian strukturalnych zostanie przeprowadzona w oparciu o Polską Klasyfikacje Dzialalności (NACE), na podstawie danych publikowanych przez Glowny Urząd Statystyczny i Eurostat.
Discussiones Mathematicae Probability and Statistics, 2008
Stȩpniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner pa... more Stȩpniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the corresponding matrices A 2 and B 2 , in the sense of the Löwner partial ordering, the star partial ordering, the minus partial ordering, and the sharp partial ordering. Many papers have since been published (mostly coauthored by J.K. Baksalary-to whom the present paper is dedicated) that generalize the results in two directions: by widening the class of matrices considered and by replacing the squares by arbitrary powers. In the present paper we make a résumé of some of these results and suggest some further generalizations for polynomials of the matrices considered.
Sang-Il Lee (2001, 2004) developed and analysed a new bivariate spatial association measure (cite... more Sang-Il Lee (2001, 2004) developed and analysed a new bivariate spatial association measure (cited by many authors who discussed the measure from theoretical as well as practical point of view). He noted that “a bivariate spatial association measure should be a composite of three elements: univariate spatial associations of two variables and their point-to-point association in a certain form”. The idea led him to construction the bivariate measure L connected with decomposition of Moran’s I. The L statistics integrates Pearson’s r and Moran’s I and heavily depends on (introduced by Sang-Il Lee) a spatial smoothing scalar (SSS). In the paper we examine some results obtained by Sang-Il Lee dropping (changing) some theoretical assumption used in the definition (decomposition) of L.
Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013
We consider two linear models, M 1 = {y, Xβ, V 1 } and M 2 = {y, Xβ, V 2 }, having different cova... more We consider two linear models, M 1 = {y, Xβ, V 1 } and M 2 = {y, Xβ, V 2 }, having different covariance matrices. Our main interest lies in question whether a particular given BLUE under M 1 continues to be a BLUE under M 2. We give a thorough proof of a result originally due to Mitra and Moore (Sankhyā, Ser. A 35:139-152, 1973). While doing this, we will review some useful properties of the proper eigenvalues in the spirit of Rao and Mitra (Generalized Inverse of Matrices and Its Applications, 1971).
Analysis of the Labour Market in Metropolitan Areas: A Spatial Filtering Approach The power of to... more Analysis of the Labour Market in Metropolitan Areas: A Spatial Filtering Approach The power of today's computers allows us to perform computation on massive quantities of data on the one hand and produces enormous amounts of analysis output on the other, as noted by Griffith in his 2003 book. Besides, visualisation and spatial filtering (the core of considerations in Griffith's book) have a chance to be widely used in research practice, especially in geosciences and, more precisely, for georeferenced data. Following the idea proposed by Patuelli et al. (2006, 2009), we analysed the labour market in Poland, focusing on metropolitan areas and their surroundings. The analysis was performed on a data set for the unemployment rate in the 2,478 Polish communes. We took into account spatial autocorrelation and used spatial filtering techniques to construct components of an orthogonal map pattern. As shown in Tiefelsdorf & Griffith (2007), the spatial filtering techniques could be e...
Communications in Statistics - Theory and Methods, 2012
In this article, we consider two linear models, 1 = y X V 1 and 2 = y X V 2 , which differ only i... more In this article, we consider two linear models, 1 = y X V 1 and 2 = y X V 2 , which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X under these models. The corresponding problems between the models y X I n and y X V , i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X under 1 and 2. This article is an expository one presenting also new results.
The distributional properties of the Moran coefficient index (MC) measuring spatial autocorrelati... more The distributional properties of the Moran coefficient index (MC) measuring spatial autocorrelation were investigated by many authors, see eg [1]. The properties of MC for non-normal random variables were analysed by Griffith in [2]. The general idea of that paper was to extend Pitman-Koopmans theorem for the mean and the variance of this index. The principal conclusion was that under independence assumption and big enough sample size the Pitman-Koopmans theorem results can be extended to some non-normal random ...
The distributional properties of the Moran coecient index (MC) measuring spatial autocorrelation ... more The distributional properties of the Moran coecient index (MC) measuring spatial autocorrelation were investigated by many authors, see e.g. [1]. The properties of MC for non-normal random variables were analysed by Grith in [2]. The general idea of that paper was to extend Pitman-Koopmans theorem for the mean and the variance of this index. The principal conclusion was that under independence assumption and big enough sample size the Pitman-Koopmans theorem results can be extended to some non-normal random variables. The independence and identically distributed property reduced the necessary sample size for this extension, as did the properties of symmetry and normal approximation. In the paper we continue the analysis performing simulations for randomly generated variables for the following distributions: beta, gamma, hypergeometric, inverse hypergeometric, log-normal, exponential, negative binomial, and t Student, as well as their mixtures and using Box-Cox power transformation.
Distance learning in all types of schools from March 2020 to the beginning of June 2021 (with a s... more Distance learning in all types of schools from March 2020 to the beginning of June 2021 (with a short break in September 2020) was forced by the COVID-19 pandemic. Previously, in Poland, this form of teaching was used sporadically, basically only for extra-curricular activities. The vast majority of teachers did not have any experience in this field. The large-scale introduction of new forms of distance learning and knowledge transfer and enforcement methods created a number of challenges and opened up new opportunities. The presented study attempts to identify the advantages and disadvantages of distance learning during the COVID-19 pandemic in the opinion of primary and secondary school teachers in the Wielkopolska region. The analysis was carried out based on empirical material obtained from questionnaires addressed to all teachers from the Wielkopolska region (703 questionnaires were received). The survey results allowed the diagnosis of positive and negative aspects of distance...
Introduction The anterolateral thigh flap (ALT) is one of the most commonly used grafts in head a... more Introduction The anterolateral thigh flap (ALT) is one of the most commonly used grafts in head and neck reconstructive surgery. In this type of surgery, it is essential that the vascular pedicle be long enough to ensure proper vascular anastomosis. However, it is difficult to accurately estimate the pedicle length preoperatively. In this context, the current study had two aims: (1) to assess the value of colour Doppler sonography (CDS) in the preoperative assessment of the vascular pedicle and (2) to develop a mathematical model to predict the length of the vascular pedicle based on the ultrasound findings. Materials and methods Retrospective review of patients who underwent primary surgery for head and neck cancer followed by ALT flap reconstruction at our institution from 2014 to 2018. All patients underwent CDS prior to surgical excision of the flap. Results Preoperative CDS was useful to identify the location of the vascular perforators, to estimate the pedicle length, and to identify the vascularization variant. Using the proposed mathematical formula, the estimated minimum pedicle length and actual length agreed in 73.9% of cases, increasing to 84.1% when a 5 mm margin of error was allowed. Moreover, preoperative ultrasound accurately distinguished the two anatomical variants of the ALT vasculature in nearly all cases (97.1%). Conclusion This study confirms the value of preoperative colour Doppler sonography for ALT flap reconstruction. The proposed mathematical model provides a highly accurate method of preoperatively assessing the length of the vascular pedicle, which may be of value in head and neck surgery.
Rozwój Regionalny i Polityka Regionalna, Mar 20, 2014
Zastosowanie metod taksonomicznych w analizie struktury systemu regionalnego Zarys treści: Celem ... more Zastosowanie metod taksonomicznych w analizie struktury systemu regionalnego Zarys treści: Celem pracy jest zastosowanie metod taksonomii numerycznej w badaniu makrostruktury regionalnej i ocena ich możliwości analitycznych. W pierwszej części pracy przedstawiono opis matematyczno-statystyczny dwóch metod: (1) metody delimitacji układów powiązań opartej na kryterium największego przepływu Nystuena i Daceya (1961), (2) metody identyfikacji istotnych relacji w systemie regionalnym na zasadzie maksymalizacji współczynnika determinacji, opracowanej przez Holmesa i Haggetta (1977). W drugiej części pracy wykorzystano równolegle proponowane metody dla określenia makrostruktury regionalnej Polski na podstawie międzyregionalnych przepływów migracyjnych. Dokonano również oceny wyników poznawczych uzyskanych w analizie makrostruktury regionalnej w aspekcie metodologicznym i empiryczno-diagnostycznym.
The findings presented in this paper are part of the comprehensive research carried out within th... more The findings presented in this paper are part of the comprehensive research carried out within the “Diversification of Social Attitudes in the Sphere of Educational Services during a Pandemic” project. This study examines the challenges that emerged during remote learning, focusing on parents’ involvement in their children’s learning process, as perceived by school principals. The conclusions are based on questionnaire interviews with principals of 36 randomly selected schools throughout the Wielkopolska region (Poland). The study spanned the second semester of the 2019/2020 school year and the first semester of 2020/2021. Several issues were identified in the interviews, including communication difficulties with students, lack of skills of teachers and students to work remotely, insufficient IT infrastructure at school and home, financial deficits impeding the purchase of new equipment, and a decline in students’ mental health. These problems were primarily related to the family (h...
Zróżnicowanie poziomu rozwoju i jego polaryzacja są silnie akcentowanymi cechami procesu rozwoju ... more Zróżnicowanie poziomu rozwoju i jego polaryzacja są silnie akcentowanymi cechami procesu rozwoju społeczno-gospodarczego zarówno w klasycznych koncepcjach rozwoju (zwłaszcza rozwoju spolaryzowanego), jak i w ich współczesnych kontynuacjach. Prowadzi to do występowania w przestrzeni ekonomicznej obszarów wzrostu i obszarów stagnacji gospodarczej. Dlatego niezwykle istotne jest poszukiwanie odpowiedzi na pytania dotyczące przyczyn zróżnicowań układów przestrzennych oraz procesów polaryzacji. Głównym celem pracy jest identyfikacja i analiza istotnych czynników determinujących rozmieszczenie oraz rozwój obszarów wzrostu i obszarów stagnacji gospodarczej w ujęciu całościowym i częściowym rozwoju, w układzie wybranych aspektów tego procesu. Procedurę identyfikacji czynników rozwoju oparto na analizie korelacji kanonicznych (ujęcie całościowe) oraz modelowaniu regresyjnym (ujęcie częściowe). Postępowanie badawcze przeprowadzono zarówno w układzie wszystkich powiatów, jak i ich specyficznych podukładów, tj. obszarów wzrostu i obszarów stagnacji gospodarczej. Słowa kluczowe: obszary wzrostu, obszary stagnacji, czynniki rozwoju, analiza kanoniczna, analiza regresji Wstęp Zróżnicowanie poziomu rozwoju i jego polaryzacja są silnie akcentowanymi cechami procesu rozwoju społeczno-gospodarczego zarówno w klasycznych koncepcjach rozwoju (zwłaszcza rozwoju spolaryzowanego), jak i w ich współczesnych kontynuacjach (por. Grzeszczak 1999, Churski 2011). Konsekwencją nasilających się procesów polaryzacji jest występowanie w przestrzeni ekonomicznej obszarów wzrostu i obszarów stagnacji gospodarczej (por. Churski 2013a). Dlatego niezwykle istotne jest poszukiwanie odpowiedzi na pytania 1 Artykuł powstał w ramach projektu badawczego "Rozwój społeczno-gospodarczy a kształtowanie się obszarów wzrostu i obszarów stagnacji gospodarczej" finansowanego ze środków Narodowego Centrum Nauki (N N306 791940), realizowanego przez zespół badawczy pracowników Zakładu Analizy Regionalnej Instytutu Geografii Społeczno-Ekonomicznej i Gospodarki Przestrzennej, którego członkami są autorzy.
Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic ac... more Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic activity based on geolocations of firms. The aim of the paper is to introduce theoretical backgrounds of SPAG. The measure is a product of two random variables with beta and gamma distributions. The moments of the product are described and estimated for Poland with spatial centroids of LAU2 treated as geolocations of firms for empirical distribution as well as for the set of firms located in a regular region. Another approach to SPAG properties has its origin in a geometric probability concept. We present the research results on geometric probability, applied to SPAG, as distance probability distributions for a regular region.
Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic ac... more Kopczewska (2017) proposed a new empirical measure of spatial agglomeration (SPAG) of economic activity based on geolocations of firms. The aim of the paper is to introduce theoretical backgrounds of SPAG. The measure is a product of two random variables with beta and gamma distributions. The moments of the product are described and estimated for Poland with spatial centroids of LAU2 treated as geolocations of firms for empirical distribution as well as for the set of firms located in a regular region. Another approach to SPAG properties has its origin in a geometric probability concept. We present the research results on geometric probability, applied to SPAG, as distance probability distributions for a regular region.
To study urban heat island (UHI), Landsat 5 TM data and in situ measurements of air temperature f... more To study urban heat island (UHI), Landsat 5 TM data and in situ measurements of air temperature from nine points in Poznań (Poland) for the period June 2008-May 2013 were used. Based on data from measurement points located in different types of land use, the surface urban heat island (SUHI) maps were created. All available and qualitycontrolled Landsat 5 TM images from 15 unique days were used to obtain the characteristics of land surface temperature (LST) and UHI intensity. In addition, spatial analysis of UHI was conducted on the basis of Corine Land Cover 2006 dataset. In situ measurements at a height of 2 m above ground level show that the UHI is a common occurrence in Poznań with a mean annual intensity of 1.0°C. The UHI intensity is greater during the warm half of the year. Moreover, results based on the remote sensing data and the Corine Land Cover 2006 indicate that the highest value of the mean LST anomalies (3.4°C) is attained by the continuous urban fabric, while the lowest value occurs within the broad-leaved forests (−3.1°C). To recount from LST to the air temperature at a height of 2 m above ground level (T agl), linear and non-linear regression models were created. For both models, coefficients of determination equal about 0.80, with slightly higher value for the non-linear approach, which was applied to estimate the T agl spatial variability over the city of Poznań.
Contemporary changes of socioeconomic development factors. The aim of the work is to determine th... more Contemporary changes of socioeconomic development factors. The aim of the work is to determine the scope of contemporary changes of socioeconomic development factors, paying attention to the consequences for their interpretation and mechanism of impact relating to the regional and local level. The main goal is specified by formulating the following research questions: (1) What major megatrends shape contemporary developmental transformations? (2) What is the direction and scope of changes in socioeconomic development factors? (3) How are the conditions of development processes changing as a result of these changes and how they differentiate the processes of development in space? The article is a synthesis of the results of two research projects of the National Science Center: NN 306 79 19 40: Socioeconomic development and the development of areas of growth and areas of economic stagnation (2011–2014) and OPUS 10 – 2015/19/B/HS5/00012: New challenges of regional policy in shaping the factors of socioeconomic development of less developed regions (2016–2019) and the results of own authors' research – employees of the Regional Analysis Department at the Institute of SocioEconomic Geography and Spatial Management of the Adam Mickiewicz University in Poznań.
W artykule przedstawiono zastosowanie entropijnej statystyki Shannona i algorytmu opracowanego pr... more W artykule przedstawiono zastosowanie entropijnej statystyki Shannona i algorytmu opracowanego przez Semple’a i Gauthier w badaniu zmian w zróżnicowaniuregionalnym Polski. Dokonano oceny wartości poznawczej tej metody ze względu na możliwość analizy relacji między nierównościami między- i wewnątrzregionalnymi.The article presents the use of Shannon entropy statistics and algorithm developed by Semple and Gauthier in the study of changes in the Polish regional differences. The assessment of the cognitive value of this method due to the possibility of analyzing the relationship between inter- and intraregional inequalities is shown
Dynamicznemu rozwojowi uslug, jaki nastepuje w Polsce od początku lat 90. XX w., towarzyszą przem... more Dynamicznemu rozwojowi uslug, jaki nastepuje w Polsce od początku lat 90. XX w., towarzyszą przemiany związane ze strukturą sektora uslug. Analiza zmian zachodzących w gospodarce prowadzi do wniosku, ze coraz wiekszego znaczenia w sektorze uslug nabierają uslugi wyspecjalizowane, zatrudniające pracownikow o wysokich kwalifikacjach zawodowych, wśrod nich uslugi o wysokim nasyceniu wiedzą oraz grupa uslug dla producentow i dla biznesu. Celem pracy jest prezentacja przemian zachodzących w sektorze uslug w Polsce na tle innych panstw Europy. Analiza zmian strukturalnych zostanie przeprowadzona w oparciu o Polską Klasyfikacje Dzialalności (NACE), na podstawie danych publikowanych przez Glowny Urząd Statystyczny i Eurostat.
Discussiones Mathematicae Probability and Statistics, 2008
Stȩpniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner pa... more Stȩpniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the corresponding matrices A 2 and B 2 , in the sense of the Löwner partial ordering, the star partial ordering, the minus partial ordering, and the sharp partial ordering. Many papers have since been published (mostly coauthored by J.K. Baksalary-to whom the present paper is dedicated) that generalize the results in two directions: by widening the class of matrices considered and by replacing the squares by arbitrary powers. In the present paper we make a résumé of some of these results and suggest some further generalizations for polynomials of the matrices considered.
Sang-Il Lee (2001, 2004) developed and analysed a new bivariate spatial association measure (cite... more Sang-Il Lee (2001, 2004) developed and analysed a new bivariate spatial association measure (cited by many authors who discussed the measure from theoretical as well as practical point of view). He noted that “a bivariate spatial association measure should be a composite of three elements: univariate spatial associations of two variables and their point-to-point association in a certain form”. The idea led him to construction the bivariate measure L connected with decomposition of Moran’s I. The L statistics integrates Pearson’s r and Moran’s I and heavily depends on (introduced by Sang-Il Lee) a spatial smoothing scalar (SSS). In the paper we examine some results obtained by Sang-Il Lee dropping (changing) some theoretical assumption used in the definition (decomposition) of L.
Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013
We consider two linear models, M 1 = {y, Xβ, V 1 } and M 2 = {y, Xβ, V 2 }, having different cova... more We consider two linear models, M 1 = {y, Xβ, V 1 } and M 2 = {y, Xβ, V 2 }, having different covariance matrices. Our main interest lies in question whether a particular given BLUE under M 1 continues to be a BLUE under M 2. We give a thorough proof of a result originally due to Mitra and Moore (Sankhyā, Ser. A 35:139-152, 1973). While doing this, we will review some useful properties of the proper eigenvalues in the spirit of Rao and Mitra (Generalized Inverse of Matrices and Its Applications, 1971).
Analysis of the Labour Market in Metropolitan Areas: A Spatial Filtering Approach The power of to... more Analysis of the Labour Market in Metropolitan Areas: A Spatial Filtering Approach The power of today's computers allows us to perform computation on massive quantities of data on the one hand and produces enormous amounts of analysis output on the other, as noted by Griffith in his 2003 book. Besides, visualisation and spatial filtering (the core of considerations in Griffith's book) have a chance to be widely used in research practice, especially in geosciences and, more precisely, for georeferenced data. Following the idea proposed by Patuelli et al. (2006, 2009), we analysed the labour market in Poland, focusing on metropolitan areas and their surroundings. The analysis was performed on a data set for the unemployment rate in the 2,478 Polish communes. We took into account spatial autocorrelation and used spatial filtering techniques to construct components of an orthogonal map pattern. As shown in Tiefelsdorf & Griffith (2007), the spatial filtering techniques could be e...
Communications in Statistics - Theory and Methods, 2012
In this article, we consider two linear models, 1 = y X V 1 and 2 = y X V 2 , which differ only i... more In this article, we consider two linear models, 1 = y X V 1 and 2 = y X V 2 , which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X under these models. The corresponding problems between the models y X I n and y X V , i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X under 1 and 2. This article is an expository one presenting also new results.
The distributional properties of the Moran coefficient index (MC) measuring spatial autocorrelati... more The distributional properties of the Moran coefficient index (MC) measuring spatial autocorrelation were investigated by many authors, see eg [1]. The properties of MC for non-normal random variables were analysed by Griffith in [2]. The general idea of that paper was to extend Pitman-Koopmans theorem for the mean and the variance of this index. The principal conclusion was that under independence assumption and big enough sample size the Pitman-Koopmans theorem results can be extended to some non-normal random ...
Properties of eigenvalues of matrices used in statistical analysis provide an important base in t... more Properties of eigenvalues of matrices used in statistical analysis provide an important base in the description of statistical properties within analyzed problem. The paper extends some characterizations of diagonalizable matrices whose sum has nonnegative eigenvalues. In the paper there are presented some general comments as well as examples of matrices from speci c subsets.
Sang-Il Lee (2001, 2004) developed and analysed a new bivariate spatial association measure (cite... more Sang-Il Lee (2001, 2004) developed and analysed a new bivariate spatial association measure (cited by many authors who discussed the measure from theoretical as well as practical point of view). He noted that “a bivariate spatial association measure should be a composite of three elements: univariate spatial associations of two variables and their point-to-point association in a certain form”. The idea led him to construction the bivariate measure L connected with decomposition of Moran’s I.
The L statistics integrates Pearson’s r and Moran’s I and heavily depends on (introduced by Sang-Il Lee) a spatial smoothing scalar (SSS). In the paper we examine some results obtained by Sang-Il Lee dropping (changing) some theoretical assumption used in the definition (decomposition) of L.
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Papers by Jan Hauke
The L statistics integrates Pearson’s r and Moran’s I and heavily depends on (introduced by Sang-Il Lee) a spatial smoothing scalar (SSS). In the paper we examine some results obtained by Sang-Il Lee dropping (changing) some theoretical assumption used in the definition (decomposition) of L.